Lecture Notes in Computer Science 3472

300 Christophe Gaston and Dirk Seifert
computations). In some cases, a data flow graph can be seen as an annotated
control flow graph.
In the following, a flow graph is a representation of all statement sequences
of the model, and a test case is a possible (instantiated) instance of a path in
the flow graph (i.e., inputs which execute the instruction sequence denoted by
the path) [ZHM97]. Moreover each occurrence of a variable in a node is classified
either as definition occurrence or as use occurrence. The latter can be further
divided into computational use or, if it is used within a predicate, into predicate
use. In the following necessary definitions are given:
• A definition clear path with respect to a variable x in a flow graph is a path
where for all nodes in the path there is no definition occurrence of x .
• A definition occurrence of variable x within a node u reaches a computational
use occurrence of x within a node v, if and only if there is a path p =
(u, w1,...,wn, v), such that (w1,...,wn) is definition clear with respect to x .
• A definition occurrence of variable x in u reaches a predicate use occurrence
of x on the edge (wn, v), if and only if there is a path p =(u, w1,...,wn, v),
such that (w1,...,wn) is definition clear with respect to x and there exist a
predicate occurrence of x associated to the edge from wn to v.
• For both predicate and computational use occurrence, a definition occurrence
of x in u feasibly reaches the use occurrence of x , if and only if there is a
path p, such that there exists inputs which enforce the execution of p.
The simplest data flow criteria rely on paths that start with the definition of
a variable and end with the use of the same variable. The following criteria are
adapted from the work of Frankl and Weyuker [FW88].
AtestsuiteT satisfies the all definitions coverage criterion, if and only if
for all definition occurrences of a variable x , such that there is a use occurrence of
x which is feasibly reachable from the definition, there is at least one element in T
which is a numerical instance of a path p, that contains a sub path through which
the definition of x reaches some use occurrence of x . Thus, the all definitions
coverage criterion ensures that all defined variables will be tested at least once
by one of their uses in the model. However, this is insufficient as tester require
to test all uses of all variable definitions. It is ensured by the all uses criterion.
AtestsuiteT satisfies the all uses coverage criterion, if and only if for all
definition occurrences of a variable x and for all use occurrences of x which are
feasibly reachable from the definition, there is at least one element in T which
is a numerical instance of a path p that contains a sub path through which the
definition of x reaches the use occurrence.
The previously described criteria have been specialized to take into account
that a use occurrence can be a computational use or a predicate use [RW85].
However, the all uses coverage criterion does not ensure that all possible ways
to reach a use occurrence have been tested. As there may be several sub paths
which allow a definition occurrence of a variable to reach a use occurrence of this
variable. Note that some of these paths may be infinite due to cycles and cannot
be covered. A possible solution is to restrain to cycle free sub paths. The only